Residue theorem

Hey guys.
So I got this integral I need to solve, of curse using the residue theorem.
The thing is, that I don't understand the curve.
I know that whenever Z^2 = integer, this function has a singularity point because e^(2*pi*i*n) = 1.
But again, I'm not sure what this curve has enclosed in.

This is, actually, an "infinite sequence" of problems! Each path is a circle, with center (0,0) of radius R which lies between [itex]\sqrt{n}[/itex] and [itex]\sqrt{n+1}[/itex] for each positive integer n. I suspect that you will find that the number of poles inside each path depends on n.